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12. Suppose that a, b e R and a < b. Show that the vector space C[a, b] of all continuous complex valued functions defined on a, b, with supremum norm || fllo = sup |f(t)l, tela,b) is a Banach space.

12. Suppose that a, b e R and a < b. Show that the vector space C[a, b] of all continuous complex valued functions defined on a, b, with supremum norm || fllo = sup |f(t)l, tela,b) is a Banach space.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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12. Suppose that a, b e R and a < b. Show that the vector space C[a, b] of all continuous complex valued functions defined on a, b, with supremum norm || fllo = sup |f(t)\, tela,b) is a Banach space.
Transcribed Image Text:12. Suppose that a, b e R and a < b. Show that the vector space C[a, b] of all continuous complex valued functions defined on a, b, with supremum norm || fllo = sup |f(t)\, tela,b) is a Banach space.
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